Advances in Applied Clifford Algebras

, Volume 20, Issue 2, pp 247–254 | Cite as

Finding 3 × 3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues

Article

Abstract.

We show that any 3-component octonionic vector which is purely imaginary, but not quaternionic, is an eigenvector of a 6-parameter family of Hermitian octonionic matrices, with imaginary eigenvalue equal to the associator of its elements.

Keywords.

Octonions Hermitian matrices imaginary eigenvalues 

Copyright information

© Birkhäuser / Springer Basel AG, Switzerland 2010

Authors and Affiliations

  1. 1.Department of Science and Mathematics EducationOregon State UniversityCorvallisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA

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